There's an extension called floccus [1] that can sync bookmarks between numerous different browsers (including both Firefox/Gecko and Chromium/Blink based browsers, mobile and desktop) and plug into a user-controlled NextCloud [2] or Linkwarden [3] instance running on a local homelab server for backups.
However, I try to minimize the number of installed extensions to reduce my own browser fingerprint. As others have replied, Firefox Sync works across most of today's popular downstream shadow-forks of Firefox (as in, forks that shadow the Firefox releases rather than truly forking the code). If you don't want to give Mozilla's enshittified corpse your email (I don't), just use an email service that supports aliases to sign up for Firefox Sync... Which is in any case a good idea generally: no two of your important online accounts should point to the same email, even if behind the scenes the aliases are all routing emails back to you.
However, I try to minimize the number of installed extensions to reduce my own browser fingerprint. As others have replied, Firefox Sync works across most of today's popular downstream shadow-forks of Firefox (as in, forks that shadow the Firefox releases rather than truly forking the code). If you don't want to give Mozilla's enshittified corpse your email (I don't), just use an email service that supports aliases to sign up for Firefox Sync... Which is in any case a good idea generally: no two of your important online accounts should point to the same email, even if behind the scenes the aliases are all routing emails back to you.
[1]: https://floccus.org/
[2]: https://nextcloud.com/
[3]: https://linkwarden.app/